Details
| Originalsprache | Englisch |
|---|---|
| Fachzeitschrift | Quantum |
| Jahrgang | 3 |
| Publikationsstatus | Veröffentlicht - 20 Mai 2019 |
| Extern publiziert | Ja |
Abstract
Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lowerdimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Atom- und Molekularphysik sowie Optik
- Physik und Astronomie (insg.)
- Physik und Astronomie (sonstige)
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in: Quantum, Jahrgang 3, 20.05.2019.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
AU - Stephen, David T.
AU - Nautrup, Hendrik Poulsen
AU - Bermejo-Vega, Juani
AU - Eisert, Jens
AU - Raussendorf, Robert
N1 - Funding Information: This work is supported by the NSERC (DTS, RR), Cifar (RR), the Stewart Blusson Quantum Matter Institute (RR), the European Union through the ERC grants TAQ (JBV, JE) and WASCOSYS (DTS), the DFG CRC 183 (JE), and the Austrian Science Fund FWF within the DK-ALM: W1259-N27 (HPN). DTS thanks N. Schuch for discussions, and H. Dreyer for discussions and help in preparation of the manuscript. RR thanks the American Institute of Mathematics for their hospitality during the workshop “Arithmetic golden gates” in 2017.
PY - 2019/5/20
Y1 - 2019/5/20
N2 - Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lowerdimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.
AB - Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lowerdimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.
UR - http://www.scopus.com/inward/record.url?scp=85093829112&partnerID=8YFLogxK
U2 - 10.22331/q-2019-05-20-142
DO - 10.22331/q-2019-05-20-142
M3 - Article
AN - SCOPUS:85093829112
VL - 3
JO - Quantum
JF - Quantum
SN - 2521-327X
ER -